David Fincher has given The Girl With the Dragon Tattoo a very serious software and operating system upgrade. This new English-language remake, – based on Stieg Larsson's bestselling crime novel – is sleeker, smoother, sexier than its Swedish predecessors. It is a muscular, overwhelmingly confident movie – and its brutal violence is thus even tougher to take.

Now it is Daniel Craig playing Mikael Blomkvist, the investigative journalist in Stockholm called in by a mysterious industrialist (Christopher Plummer) from a remote northern island to solve the decades-old mystery of his missing niece. Looking into this cold case is to involve the uncovering of serial killings and Sweden's sinister wartime history of Nazi sympathisers. And Blomkvist has an extraordinary assistant: Lisbeth (Rooney Mara), a dragon-tattooed computer hacker endowed with savant genius and some very serious attitude.

Nothing in the movie quite matches the terrific opening credit sequence: a Bondish, nightmarish, amorphous vision in liquid monochrome, with an eardrum-frazzling score by Trent Reznor and Atticus Ross. The rest of the film is relatively conventional by comparison, and however stylishly Fincher retools it, the basic story still looks a bit strained and awkward, with a murder mystery that somehow never quite inhabits the centre of the film – far less compelling, for me, than Fincher's Zodiac – and a final sequence that is pure Mission: Impossible.

Yet set against that is the very potent performance by Rooney Mara as Lisbeth. Audiences may remember her powerful cameo in Fincher's The Social Network as Mark Zuckerberg's angry ex-girlfriend Erica. As the girl with the dragon tattoo, she is absolutely lethal, an implacable avenger and a black-belt sexual presence. Where Noomi Rapace's Lisbeth was sometimes mysterious, often acting from behind a Gothy curtain of hair, Rooney is more explicit, more aggressive, with an asymmetric fringe taking the jet-black hair away from her pale, fierce face, and her blond-dyed eyebrows making the eyes stand out starkly, almost on stalks. Rooney's performance conveys Lisbeth's rage at the way she has been abused and raped by men, and shows how this has enabled her to help Blomkvist intuit the truth behind the misogynist hate-crimes. Yet there is something poignant in the way her badass attitude melts into love for Blomkvist himself, obscurely and ambiguously triggered by his talking about his daughter.

It is Mara who is the driving force behind this film: without her, audiences might be forced to focus on the persistently improbable and unreal-looking elements, particularly the sketchily imagined world of media and business. The uproarious final revenge taken by Lisbeth, who turns out to be a master of disguise, is a caperish ending slightly out of joint with the grim world of Nazis, rapists and serial killers. But it is a testament to Mara's massive star firepower that she powers through all this. Fincher's Dragon Tattoo rockets through the freezing northern European landscape like the most powerful car on the market.

• This article was amended on 23 December 2011. The credit list in the above box included people who worked on the Swedish adaptation of The Girl With the Dragon Tattoo. This has been corrected.